Question

verify that x³ + y³ + z³-3xyz = ½ (x+y+z)(x-y)²+(y-2)²+(z-x)²}


subject maths
please answer​

Answer 1

Solving R.H.S

1/2 (x+y+z)[(x - y)² + (y- z)² + (z − x)²]

Using (a - b)2 = a² + b² - 2ab

= (x + y + z) [ (x² + y² − 2xy) + (y² + z² − 2yz) + (z² + x² – 2zx)]

=(x + y + z) [2x² + 2y² + 2z² - 2xy-2yz - 2zx]

= (x+y+z) 2 [x² + y² + z² - xy - yz - zx]

= (x+y+z) [x² + y² + z² - xy-yz-zx]

We know x³ + y² + z³ - 3xyz = (x+y+z) (x² + y² + z²-xy-yz - zx)

= x³ + y³ + z³ - 3xyz

= L.H.S

Hence proved